Only first order ordinary differential equations can be solved by using the Runge Kutta 4th order method. It serves as an exceptional text for self-study as well as resource for general reference. The Runge-Kutta method finds approximate value of y for a given x. In introducing each numerical method, Engineering Analysis gives minimum mathematical derivations but provides a thorough explanation of computational procedures to solve a specific problem. The book emphasizes interactive operation in developing computer programs throughout, enabling the values of the parameters involved in the problem to be entered by the user of the program via a keyboard. provides an introduction to MATLAB and Mathematica, enabling readers to write supplementary m-files for MATLAB and toolkits for Mathematica using C-like commands.teaches readers to become proficient in FORTRAN or QuickBASIC programming to solve engineering problems.numerical solution of ordinary differential equations.numerical computation of single and double integrals.finite differences and methods for interpolation and numerical differentiation.methods for finding the roots of polynomials and transcendental equations.7 For a sufficiently small Runge-Kutta timestep dt. In the following short equivalent programs, one in Fortran and one in C, we use the 'classic' fourth-order Runge-Kutta integration algorithm to solve the one-dimensional harmonic oscillator problem. This book provides a concise introduction to numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate the examples. The best general-purpose integrator is the self-starting fourth-order Runge-Kutta algorithm.

Fortran program for runge kutta method